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Feichtinger Conjectures, $R_varepsilon$-Conjectures and Weaver's Conjectures for Banach spaces | | K. Mahesh Krishna
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1 Jan 2022 | | Abstract: | Motivated from two decades old famous Feichtinger conjectures for frames,
$R_varepsilon$-conjecture and Weaver’s conjecture for Hilbert spaces (and
their solution by Marcus, Spielman, and Srivastava), we formulate Feichtinger
conjectures for p-approximate Schauder frames, $R_varepsilon$-conjecture,
Weaver’s conjectures and Akemann-Weaver conjectures for Banach spaces. We also
formulate conjectures on p-approximate Schauder frames based on the results of
Casazza for frames for Hilbert spaces. We state conjectures and problems for
p-approximate Schauder frames based on fundamental inequality for frames for
Hilbert spaces and scaling problem for Hilbert space frames. Based on
Kothe-Lorch theorem for Riesz bases for Hilbert spaces, we formulate a problem
for p-approximate Riesz bases for Banach spaces. We formulate dynamical
sampling problem for p-approximate Schauder frames for Banach spaces. We ask
phase retrieval problem and norm retrieval problem for p-approximate Schauder
frames for Banach spaces. We also formulate discretization problem for
continuous p-approximate Schauder frames. | | Source: | arXiv, 2201.00125 | | Services: | Forum | Review | PDF | Favorites | |
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